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    Possible Observation of Quadrupole Waves in Spin Nematics

    Jieming Sheng1,2,*, Jiahang Hu3,4,*, Lei Xu5, Le Wang1,6, Xiaojian Shi7,5, Runze Chi3,4,8, Dehong Yu9, Andrey Podlesnyak10, Pharit Piyawongwatthana11 et al.

    Naoki Murai11, Seiko Ohira-Kawamura11, Huiqiu Yuan7,5, Ling Wang5, Jia-Wei Mei1,6,12,†, Hai-Jun Liao3,13,‡, Tao Xiang3,4,14,§, Liusuo Wu1,15,∥, and Zhentao Wang7,5,¶

    • *These authors contributed equally to this work.
    • †Contact author: meijw@sustech.edu.cn
    • ‡Contact author: navyphysics@iphy.ac.cn
    • §Contact author: txiang@iphy.ac.cn
    • ∥Contact author: wuls@sustech.edu.cn
    • Contact author: ztwang@zju.edu.cn

    Phys. Rev. Lett. 135, 156704 – Published 9 October, 2025Erratum Phys. Rev. Lett. 136, 209901 (2026)

    DOI: https://doi.org/10.1103/pywx-vxfh

    Abstract

    Discovery of new states of matter is a key objective in modern condensed matter physics, which often leads to revolutionary technological advancements such as superconductivity. Quantum spin nematic, a “hidden order” that evades conventional magnetic probes, is one such state. Na2BaNi(PO4)2 is a potential spin nematic material, suggested by the observation of a two-magnon Bose-Einstein condensation from above the saturation field. However, direct confirmation of the spin nematicity remains elusive. This Letter presents inelastic neutron scattering spectra from the putative spin nematic phases of Na2BaNi(PO4)2, revealing low-energy quadrupole waves that are absent in the neighboring conventional magnetic phases. A spin-one model quantitatively captures the full details of the spin excitation spectra across all low-temperature phases, providing direct evidence of the spin nematic orders. Additionally, we show evidence of the three-magnon continuum and two-magnon bound states in the 1/3-magnetization plateau, revealing condensation of the two-magnon bound state as the origin of the low-field spin nematic supersolid phase.

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    Erratum

    Erratum: Possible Observation of Quadrupole Waves in Spin Nematics [Phys. Rev. Lett. 135, 156704 (2025)]

    Jieming Sheng, Jiahang Hu, Lei Xu, Le Wang, Xiaojian Shi, Runze Chi, Dehong Yu, Andrey Podlesnyak, Pharit Piyawongwatthana, Naoki Murai, Seiko Ohira-Kawamura, Huiqiu Yuan, Ling Wang, Jia-Wei Mei, Hai-Jun Liao, Tao Xiang, Liusuo Wu, and Zhentao Wang
    Phys. Rev. Lett. 136, 209901 (2026)

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